If my ReefLink loses connection to the internet, will I lose my programming?

The most simple answer is No.

One of the differentiating characteristics about the EcoSmart Live platform, EcoTech equipment and the Reeflink is that the ReefLink is simply a bridge between smart devices that retain their programming and the cloud where you create programs.

Your EcoSmart Live account will retain your programming until you delete them and is not dependent on the equipment to be operational or connected to save that program. In other words, your equipment will retain the programming loaded on to it until you reprogram it.